## Abstract

We give an explicit approach for Bockstein homomorphisms of the Hochschild cohomology of a group algebra and of a block algebra of a finite group and we show some properties. To give explicit definitions for these maps we use an additive decomposition and a product formula for the Hochschild cohomology of group algebras given by Siegel and Witherspoon in 1999. For an algebraically closed field *k* of characteristic *p* and a finite group *G* we prove an additive decomposition and a product formula for the cohomology algebra of a defect group of a block ideal of *kG* with coefficients in the source algebra of this block, and we define similar Bockstein homomorphisms.

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